Resistors in Series

When resistors are joined end to end, one after another, they're said to be connected in series. Insert an ammeter anywhere in a series circuit and it reads the same value, no matter where you place it — the current is the same through every resistor and every part of the circuit.

The battery's total potential difference, however, gets split across the resistors. If V₁, V₂, and V₃ are the potential differences across three series resistors, the total is their sum: V = V₁ + V₂ + V₃.

Applying Ohm's law to the whole circuit (V = IR) and to each resistor separately (V₁ = IR₁, V₂ = IR₂, V₃ = IR₃), and substituting into V = V₁ + V₂ + V₃, gives IR = IR₁ + IR₂ + IR₃. Since I is common to every term, it cancels, leaving Rs = R₁ + R₂ + R₃ — the equivalent resistance of resistors in series is simply the sum of their individual resistances, and is always greater than any one of them.

A series circuit has real drawbacks: since the same current flows everywhere, you can't put components needing very different currents (like a bulb and a heater) in series. And if one component fails, the whole circuit breaks — exactly why old-style 'fairy lights' would all go dark if a single bulb blew.